It is desired to produce an aligned carbon fiber-epoxy...

It is desired to produce an aligned carbon fiber-epoxy matrix composite having a longitudinal tensile strength of $500 \mathrm{MPa}(72,500 \mathrm{psi})$. Calculate the volume fraction of fibers necessary if (1) the average fiber diameter and length are $0.01 \mathrm{~mm}\left(3.9 \times 10^{-4}\right.$ in.) and $0.5 \mathrm{~mm}\left(2 \times 10^{-2}\right.$ in.), respectively; (2) the fiber fracture strength is $4.0$ GPa $\left(5.8 \times 10^{5} \mathrm{psi}\right)$; (3) the fiber-matrix bond strength is $25 \mathrm{MPa}$ (3625 psi); and (4) the matrix stress at composite failure is $7.0 \mathrm{MPa}$ (1000 psi).

Key Concepts

Composite Materials

Composite materials are engineered by combining two or more constituent materials to achieve superior properties compared to the individual components. The design of composites often involves a stiff, strong reinforcement embedded in a ductile matrix, allowing tailoring of strength, stiffness, and failure behavior through the manipulation of constituent properties and relative amounts.

Volume Fraction

Volume fraction is the ratio of the volume of one component, typically the reinforcement (fiber), to the total volume of the composite. It is a crucial parameter in composite design because it directly influences mechanical properties such as tensile strength and modulus, and helps in optimizing the performance of the composite material.

Fiber Mechanics

Fiber mechanics deals with the behavior and properties of the fibers used in composites, particularly their tensile or fracture strength. Since fibers are primarily responsible for carrying the load in aligned composites, understanding their strength characteristics is essential for predicting the overall composite performance and ensuring safe design.

Critical Fiber Length

Critical fiber length is the minimum length required for a fiber to develop its full tensile strength through effective load transfer from the matrix via interfacial shear. It is determined by the fiber’s fracture strength and the fiber-matrix bond strength, and it ensures that fibers contribute effectively to the composite’s overall load-bearing capacity.

Fiber-Matrix Interface Bond

The fiber-matrix interface bond represents the strength of adhesion between the fiber and the matrix. This bond is critical because it governs the efficiency of load transfer from the matrix to the fiber. A strong interfacial bond minimizes debonding and fiber pull-out, thereby enhancing the composite’s tensile strength.

Matrix Properties

Matrix properties, particularly the failure stress of the matrix, play a significant role in composite behavior. While the matrix primarily serves to support and transfer load between fibers, its strength limitations can also dictate the overall failure mode of the composite if the load exceeds the matrix’s capability, especially in regions with insufficient reinforcement.

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